A recent post on Dan Meyer’s blog began a discussion about the amount of real learning going on in math classes, contrasted with the far too frequent, unfortunate practice of memorization of procedures and rules. The Chinese room thought experiment places a person in a room with an instruction book that contains rules for transforming strings of Chinese characters into other strings of Chinese characters. Someone, outside the room, passes notes with questions in Chinese into the room, and the person in the room uses his book of rules to transform the characters and send out answers. To the person on the outside, it appears that the person in the room is a fluent Chinese speaker. Only the person in the room knows the secret: he understands neither the meanings of the questions nor the answers.
Think about your own experience in math classes. Were you the person in the room, manipulating symbols according to rules your teacher gave you, never really understanding the meaning of anything you were doing? Your teacher sees correct answers and thinks you are “learning”. But only you know the secret.
Sometimes your teachers gave you rules that weren’t even true when you moved to the next grade. You know, things like “When you multiply by ten add a zero at the end” or “Multiplication makes numbers bigger” (See the excellent free preview article from Teaching Children Mathematics on more Rules that Expire). Then you had to read a whole new book of rules to deal with different kinds of numbers and the operations we perform with them.
You might have seen Elizabeth Green’s recent New York Times Magazine article on why Americans stink at math. The conclusion? “The cognitive-science research suggested a startling cause of American’s innumeracy: school.” Mathematician Walter Sawyer put it another way: “The depressing thing about arithmetic badly taught is that it destroys a child’s intellect, and to some extent, his integrity. Before they are taught arithmetic children will not give their assent to utter nonsense; afterwards, they will.”
Working with middle school students, I see students assent to mountains of nonsense. In trying to remember all the procedures they were taught without understanding, they abandon any number sense they might have had when they were young, misapply the rules, and often arrive at totally unreasonable results.
So how do we release our students from the Chinese room to ensure that real and enduring learning is taking place? The answer comes from the National Council of Teachers of Mathematics. In their new document Principles to Actions, NCTM states:
The widespread adoption of the Common Core State Standards for Mathematics presents an unprecedented opportunity for systemic improvement in mathematics education in the United States. The Common Core State Standards offers a foundation for the development of more rigorous, focused, and coherent mathematics curricula, instruction, and assessments that promote conceptual understanding and reasoning as well as skill fluency.
Principles to Actions details eight research-based Mathematics Teaching Practices that support the teaching and learning of mathematics for all students at the highest level. If you teach math, I highly recommend a thorough review of this document during your preparation for the school year. Good luck!